MATLAB Mathematics - SERC - Index of

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6 Sparse Matrices Selected Bibliography [1] Amestoy, P. R., T. A. Davis, and I. S. Duff, “An Approximate Minimum Degree Ordering Algorithm,” SIAM Journal on Matrix Analysis and Applications, Vol. 17, No. 4, Oct. 1996, pp. 886-905. [2] Barrett, R., M. Berry, T. F. Chan, et al., Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1994. [3] Davis, T.A., Gilbert, J. R., Larimore, S.I., Ng, E., Peyton, B., “A Column Approximate Minimum Degree Ordering Algorithm,” Proc. SIAM Conference on Applied Linear Algebra, Oct. 1997, p. 29. [4] Gilbert, John R., Cleve Moler, and Robert Schreiber, “Sparse Matrices in MATLAB: Design and Implementation,” SIAM J. Matrix Anal. Appl., Vol. 13, No. 1, January 1992, pp. 333-356. [5] Larimore, S. I., An Approximate Minimum Degree Column Ordering Algorithm, MS Thesis, Dept. of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, 1998, available at http://www.cise.ufl.edu/tech_reports/ [6] Lehoucq, R. B., D. C. Sorensen, C. Yang, ARPACK Users’ Guide, SIAM, Philadelphia, 1998. [7] Saad, Yousef, Iterative Methods for Sparse Linear Equations. PWS Publishing Company, 1996. 6-44
Index A additional parameters BVP example 5-73, 5-76 adjacency matrix and graphing 6-17 Bucky ball 6-18 defined 6-17 distance between nodes 6-22 node 6-17 numbering nodes 6-19 airflow modeling 6-23 amp1dae demo 5-42 anonymous functions representing mathematical functions 4-3 arguments, additional 4-30 B ballode demo 5-28 bandwidth of sparse matrix, reducing 6-29 batonode demo 5-42 bicubic interpolation 2-12 bilinear interpolation 2-12 boundary conditions BVP 5-63 BVP example 5-70 PDE 5-91 PDE example 5-96 Boundary Value Problems. See BVP Brusselator system (ODE example) 5-25 brussode demo 5-25 Buckminster Fuller dome 6-18 Bucky ball 6-18 burgersode demo 5-42 BVP 5-61 defined 5-63 rewriting as first-order system 5-69 BVP solver 5-64 basic syntax 5-65 evaluate solution at specific points 5-72 examples boundary condition at infinity (shockbvp) 5-76 Mathieu’s Equation (mat4bvp) 5-68 multipoint terms 5-84 rapid solution changes (shockbvp) 5-73 singular terms 5-80 initial guess 5-72 multipoint terms 5-84 performance 5-67 representing problems 5-68 singular terms 5-80 unknown parameters 5-72 BVP solver properties querying property structure 5-89 C cat sparse operands 6-26 characteristic polynomial of matrix 2-4 characteristic roots of matrix 2-4 chol sparse matrices 6-26 Cholesky factorization 1-27 sparse matrices 6-33 closest point searches Delaunay triangulation 2-24 colamd minimum degree ordering 6-30 colmmd column permutation 6-31 colperm 6-29 Index-1
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MATLAB® The Language of Technical
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Revision History June 2004 First pr
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2 Polynomials and Interpolation Pol
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Introduction to Initial Value ODE P
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vi Contents
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1 Matrices and Linear Algebra Funct
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1 Matrices and Linear Algebra Matri
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1 Matrices and Linear Algebra Singu
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2 Polynomials and Interpolation Pol
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2 Polynomials and Interpolation Cal
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2 Polynomials and Interpolation whe
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2 Polynomials and Interpolation Int
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2 Polynomials and Interpolation int
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2 Polynomials and Interpolation 2 G
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2 Polynomials and Interpolation for
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2 Polynomials and Interpolation Con
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2 Polynomials and Interpolation 7 3
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2 Polynomials and Interpolation T =
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2 Polynomials and Interpolation 2-3
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2 Polynomials and Interpolation 2-3
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3 Fast Fourier Transform (FFT) Intr
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3 Fast Fourier Transform (FFT) 200
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3 Fast Fourier Transform (FFT) 2 x
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3 Fast Fourier Transform (FFT) 500
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3 Fast Fourier Transform (FFT) Func
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4 Function Functions Function Summa
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4 Function Functions You can also c
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4 Function Functions 25 20 15 10 5
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4 Function Functions Minimizing Fun
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4 Function Functions To try fminsea
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4 Function Functions Plotting the R
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4 Function Functions The number of
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4 Function Functions and displays t
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4 Function Functions end function s
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4 Function Functions States of the
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4 Function Functions 100 80 60 40 2
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4 Function Functions You can verify
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4 Function Functions Troubleshootin
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4 Function Functions A three-dimens
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4 Function Functions Parameterizing
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4 Function Functions “Anonymous F
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5 Differential Equations Initial Va
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5 Differential Equations odephas3 o
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5 Differential Equations This secti
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5 Differential Equations The basic
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5 Differential Equations 2 Code the
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5 Differential Equations function.
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5 Differential Equations One way to
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5 Differential Equations y0, yp0 Ve
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5 Differential Equations For exampl
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5 Differential Equations 1 0.8 0.6
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5 Differential Equations 2.5 Soluti
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5 Differential Equations To run thi
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5 Differential Equations 2 u′ i =
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5 Differential Equations dydt(i+1,:
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5 Differential Equations refine = 4
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5 Differential Equations Example: A
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5 Differential Equations function [
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5 Differential Equations Note The R
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5 Differential Equations 1 Robertso
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5 Differential Equations The MATLAB
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5 Differential Equations Summary of
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5 Differential Equations Problem Si
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5 Differential Equations Error Tole
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5 Differential Equations Troublesho
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5 Differential Equations Function d
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5 Differential Equations dde23 prod
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5 Differential Equations The exampl
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5 Differential Equations solution y
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5 Differential Equations Example: C
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5 Differential Equations Changing D
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5 Differential Equations BVP Functi
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5 Differential Equations two-point
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5 Differential Equations The input
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5 Differential Equations 2 Pass the
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5 Differential Equations Finding Un
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5 Differential Equations vectorized
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5 Differential Equations There is a
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5 Differential Equations 3 Solve on
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5 Differential Equations hold off T
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5 Differential Equations Note The d
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5 Differential Equations legend('An
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5 Differential Equations Here, v(1-
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5 Differential Equations solution v
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5 Differential Equations Note The D
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5 Differential Equations After disc
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5 Differential Equations The output
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5 Differential Equations Note See t
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Page 292 and 293: Index LU factorization 6-30 minimum
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